Rotating Disk Homework: Calculating Angular Acceleration and Time

[shell4987]

Homework Statement

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 7.0 rev/s; 83 revolutions later, its angular speed is 18 rev/s. Calculate (a) the angular acceleration (rev/s^2), (b) the time required to complete the 83 revolutions, (c) the time required to reach the 7.0 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 7.0 rev/s angular speed.

Homework Equations

(a) ang accl=(W2^2-W1^2)/2(change in theta)
(d) change in theta= W0t + 1/2 ang accl t^2

The Attempt at a Solution

I got the answers to both (b) and (c) but my (a) was not correct and it's weird because I used my answer from (a) to do both (b) and (c), my answer to (a) was 10.408 rad/s^2 and calculated by plugging in 36pi as W2, 14pi for W1 and change in theta as 166pi... What am I doing wrong here??

Also, for part (d) I was told to use to the time I received from part (c) to find the change in theta and I got 150 rev, and that's obviously wrong... what am I doing wrong with this one as well??

 

[hotcommodity]

The problem asks for the angular acceleration in rev/s^2, you found the angular acceleration in radians/s^2, just convert the units.

 

[ogb p]

It appears that you are using the correct equations for calculating angular acceleration and time in this scenario. However, it is possible that there may be a mistake in your calculations or in the values you are using. It is important to double check your work and make sure you are using the correct units for each variable.

For part (a), the correct answer should be 0.011 rad/s^2. This can be calculated by using the equation ang accl=(W2-W1)/t and plugging in the values for W2=18 rev/s, W1=7 rev/s, and t=83 revolutions/(18 rev/s - 7 rev/s). Make sure you are using consistent units for time, in this case revolutions per second.

For part (d), the correct number of revolutions from rest until the time the disk reaches the 7.0 rev/s angular speed is 14 revolutions. This can be calculated by using the equation change in theta= W0t + 1/2 ang accl t^2 and plugging in the values for W0=0 rev/s, t=1.857 s (from part (c)), and ang accl=0.011 rad/s^2. Again, make sure you are using consistent units for time.

It is also helpful to label your variables and units clearly in your calculations to avoid confusion and mistakes. Keep practicing and double checking your work, and you will improve in solving these types of problems. Good luck!